发布求助
文献互助 智能选刊 最新文献

Workshop on Analytic Algorithmics and Combinatorics最新文献

筛选
英文 中文
Fast Algorithm for Optimal Compression of Graphs 图的快速优化压缩算法
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.5
Yongwook Choi
{"title":"Fast Algorithm for Optimal Compression of Graphs","authors":"Yongwook Choi","doi":"10.1137/1.9781611973006.5","DOIUrl":"https://doi.org/10.1137/1.9781611973006.5","url":null,"abstract":"We consider the problem of finding optimal description for general unlabeled graphs. Given a probability distribution on labeled graphs, we introduced in [4] a structural entropy as a lower bound for the lossless compression of such graphs. Specifically, we proved that the structural entropy for the Erdos--Renyi random graph, in which edges are added with probability p, is (n2)h(p) − n log n + O(n), where n is the number of vertices and h(p) = −p log p − (1 − p) log(1−p) is the entropy rate of a conventional memoryless binary source. In this paper, we prove the asymptotic equipartition property for such graphs. Then, we propose a faster compression algorithm that asymptotically achieves the structural entropy up to the first two leading terms with high probability. Our algorithm runs in O(n + e) time on average where e is the number of edges. To prove its asymptotic optimality, we introduce binary trees that one can classify as in-between tries and digital search trees. We use analytic techniques such as generating functions, Mellin transform, and poissonization to establish our findings. Our experimental results confirm theoretical results and show the usefulness of our algorithm for real-world graphs such as the Internet, biological networks, and social networks.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115323959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On Two Distributions of Subgroups of Free Groups 关于自由群的两个子群的分布
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.11
Frédérique Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil
{"title":"On Two Distributions of Subgroups of Free Groups","authors":"Frédérique Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil","doi":"10.1137/1.9781611973006.11","DOIUrl":"https://doi.org/10.1137/1.9781611973006.11","url":null,"abstract":"We study and compare two natural distributions of finitely generated subgroups of free groups. One is based on the random generation of tuples of reduced words; that is the one classically used by group theorists. The other relies on Stallings' graphical representation of subgroups and in spite of its naturality, it was only recently considered. The combinatorial structures underlying both distributions are studied in this paper with methods of analytic combinatorics. We use these methods to point out the differences between these distributions. It is particularly interesting that certain important properties of subgroups that are generic in one distribution, turn out to be negligible in the other.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116645778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Subset Partial Order: Computing and Combinatorics 子集偏序:计算与组合
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.4
Amr Elmasry
{"title":"The Subset Partial Order: Computing and Combinatorics","authors":"Amr Elmasry","doi":"10.1137/1.9781611973006.4","DOIUrl":"https://doi.org/10.1137/1.9781611973006.4","url":null,"abstract":"Given a family F of k sets with cardinalities s1, s2, . . ., sk and N = [EQUATION], we show that the size of the partial order graph induced by the subset relation (called the subset graph) is [EQUATION], where B = log (N/ log2 N). This implies a simpler proof to the O(N2/ log2 N) bound concluded in [2]. \u0000 \u0000We also give an algorithm that computes the subset graph for any family of sets F. Our algorithm requires O(nk2/ log k) time and space on a pointer machine, where n is the number of domain elements. When F is dense, i.e. N = Θ(nk), the algorithm requires O(N2/ log2 N) time and space. We give a construction for a dense family whose subset graph is of size Θ(N2/ log2 N), indicating the optimality of our algorithm for dense families. The subset graph can be dynamically maintained when F undergoes set insertion and deletion in O(nk/ log k) time per update (that is sub-linear in N for the case of dense families). If we assume words of b ≤ k bits, allow bits to be packed in words, and use bitwise operations, the above running time and space requirements can be reduced by a factor of b log (k/b + 1)/ log k and b2 log (k/b + 1)/ log k respectively.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125961289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Preference-constrained Oriented Matching 偏好约束的定向匹配
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.9
L. Fleischer, Zoya Svitkina
{"title":"Preference-constrained Oriented Matching","authors":"L. Fleischer, Zoya Svitkina","doi":"10.1137/1.9781611973006.9","DOIUrl":"https://doi.org/10.1137/1.9781611973006.9","url":null,"abstract":"We introduce and study a combinatorial problem called preference-constrained oriented matching. This problem is defined on a directed graph in which each node has preferences over its out-neighbors, and the goal is to find a maximum-size matching on this graph that satisfies a certain preference constraint. One of our main results is a structural theorem showing that if the given graph is complete, then for any preference ordering there always exists a feasible matching that covers a constant fraction of the nodes. This result allows us to correct an error in a proof by Azar, Jain, and Mirrokni [1], establishing a lower bound on the price of anarchy in coordination mechanisms for scheduling. We also show that the preference-constrained oriented matching problem is APX-hard and give a constant-factor approximation algorithm for it.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126466924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Bivariate Asymptotics for Striped Plane Partitions 条纹平面分区的双变量渐近性
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.3
D. Panario, L. Richmond, Benjamin Young
{"title":"Bivariate Asymptotics for Striped Plane Partitions","authors":"D. Panario, L. Richmond, Benjamin Young","doi":"10.1137/1.9781611973006.3","DOIUrl":"https://doi.org/10.1137/1.9781611973006.3","url":null,"abstract":"We give a new asymptotic formula for a refined enumeration of plane partitions. Specifically: color the parts πi,j of a plane partition π according to the equivalence class of i --- j (mod 2), and keep track of the sums of the 0-colored and 1-colored parts seperately. We find, for large plane partitions, that the difference between these two sums is asymptotically Gaussian (and we compute the mean and standard deviation of the distribution). Our approach is to modify a multivariate technique of Haselgrove and Temperley.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131530298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Newton Iteration: From Numerics to Combinatorics, and Back 牛顿迭代:从数值学到组合学再回来
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.6
B. Salvy
{"title":"Newton Iteration: From Numerics to Combinatorics, and Back","authors":"B. Salvy","doi":"10.1137/1.9781611973006.6","DOIUrl":"https://doi.org/10.1137/1.9781611973006.6","url":null,"abstract":"The talk will explore a variety of old and recent algorithms whose efficiency boils down to the fast convergence of Newton iteration. Numerically, and close to the root, the number of correct digits is doubled at each iteration. When working with power series, the problem of picking a good initial point disappears and the number of coefficients is doubled at each iteration. This observation, coupled with fast multiplication, leads to fast algorithms in a variety of problems of symbolic computation, ranging from classical results on algebraic series to more recent ones on systems of differential equations.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120906148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Search Path Length of Random Binary Skip Graphs 关于随机二叉跳图的搜索路径长度
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.1
Philippe Duchon, H. Larchevêque
{"title":"On the Search Path Length of Random Binary Skip Graphs","authors":"Philippe Duchon, H. Larchevêque","doi":"10.1137/1.9781611973006.1","DOIUrl":"https://doi.org/10.1137/1.9781611973006.1","url":null,"abstract":"In this paper we consider the skip graph data structure, a load balancing alternative to skip lists, designed to perform better in a distributed environment. We extend previous results of Devroye on skip lists, and prove that the maximum length of a search path in a random binary skip graph of size n is of order log n with high probability.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127183620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Connectivity-Profile of Random Increasing k-trees 随机递增k树的连通性
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2009-10-19 DOI: 10.1137/1.9781611973006.13
Alexis Darrasse, Hsien-Kuei Hwang, O. Bodini, Michèle Soria
{"title":"The Connectivity-Profile of Random Increasing k-trees","authors":"Alexis Darrasse, Hsien-Kuei Hwang, O. Bodini, Michèle Soria","doi":"10.1137/1.9781611973006.13","DOIUrl":"https://doi.org/10.1137/1.9781611973006.13","url":null,"abstract":"Random increasing k-trees represent an interesting, useful class of strongly dependent graphs for which analytic-combinatorial tools can be successfully applied. We study in this paper a notion called connectivity-profile and derive asymptotic estimates for it; some interesting consequences will also be given.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125379689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Prediction of Unseen Proportions in Urn Models with Restricted Sampling 限制抽样下瓮模型中未见比例的预测
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2009-01-03 DOI: 10.1137/1.9781611972993.12
M. Lladser
{"title":"Prediction of Unseen Proportions in Urn Models with Restricted Sampling","authors":"M. Lladser","doi":"10.1137/1.9781611972993.12","DOIUrl":"https://doi.org/10.1137/1.9781611972993.12","url":null,"abstract":"Imagine an urn with colored balls but with an unknown composition i.e. you do not know what are the specific colors in the urn nor their relative proportions. The urn could be composed by infinitely many colors and to learn about its composition you have been sampling balls with replacement from it. In this extended abstract we will construct exact confidence intervals for the proportion in the urn of the so far unobserved colors when there is an upper-bound m for the additional number of samples permitted from the urn. The research is motivated by a variety of situations of practical interest. For instance, the different colors in the urn could represent different solutions to a particular binding site problem in a random RNA pool, or the number of different species of bacteria present in a sample of soil or the gut of a person with a digestive disorder.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117228596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Average Size of Unstretched Remote-Spanners 未拉伸遥控扳手的平均尺寸
Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2009-01-03 DOI: 10.1137/1.9781611972993.4
P. Jacquet, L. Viennot
{"title":"Average Size of Unstretched Remote-Spanners","authors":"P. Jacquet, L. Viennot","doi":"10.1137/1.9781611972993.4","DOIUrl":"https://doi.org/10.1137/1.9781611972993.4","url":null,"abstract":"Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remote-spanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for which all links in the path that are not adjacent to u belong to H. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to k-connected graphs by considering minimum length sum over k disjoint paths as distance. \u0000 \u0000In this paper, we give distributed algorithms for computing remote-spanners in order to obtain sparse remote-spanners with various properties. We provide a polynomial distributed algorithm that computes a k-connecting unstretched remote-spanner whose number of edges is at a factor 2(1 + log Δ) from optimal where Δ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O(k/n log n) in Erdos-Renyi graph model and O((k/n)2/3) in the unit disk graph model with a uniform Poisson distribution of nodes.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115379435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信